NORTHWESTERN UNIVERSITY
MECHANICAL ENGINEERING DEPARTMENT
ME 381 – Introduction to MEMS
Prof. Horacio D. Espinosa
FINAL PROJECT
Micromachined Vibrating Gyroscopes:
Design and Fabrication
Kimberly S. Elliott
Parag Gupta
Kyle B. Reed
Raquel C. Rodriguez
December 6, 2002.
TABLE OF CONTENTS
Abstract ...... 1
I. Introduction ...... 1
II. Operation Principles of Vibrating Gyroscopes ...... 1
III. Performance and Design Issues ...... 3
IV. HARPSS Vibrating Ring Gyroscope...... 4
A. Fabrication ...... 5
B. Performance ...... 6
C. Applications ...... 6
D. Limitations...... 6
V. Draper Tuning Fork Gyroscope...... 7
A. Fabrication ...... 8
B. Performance ...... 10
C. Applications ...... 10
D. Limitations...... 10
VI. Conclusions ...... 11
References ...... 11
Biographical Sketch of Group Members ...... 12
LIST OF FIGURES
- Schematic of a Vibrating Gyroscope
- Vibrating Ring Gyroscope
- Flexural Modes of Vibration
- Fabrication process for HARPSS gyroscope
- SEM view of the anchor of a poly ring gyroscope
- Voids and keyholes from polysilicon refill process
- RIE lag effect.
- (a) Coriolis Effect (b) Basic Tuning Fork
- Schematic Drawing of Draper’s Tuning Fork Gyroscope
- Dissolved Wafer, Silicon on Glass Process
0Vibrating Gyroscopes
ABSTRACT
In this paper, a review is given of the current state of the art in micromachined vibrating gyroscopes. Following a brief introduction to their basic operating principles, two case studies are discussed: a vibrating ring gyroscope designed at the University of Michigan and a tuning fork design by Draper’s Laboratory. The first is produced using high aspect-ratio polysilicon micromachining technology (HARPSS) and the second uses single-crystal silicon electrostatically bonded to glass. Performance parameters and design issues are introduced and discussed.
I. INTRODUCTION
The emergence of micromachining technology has generated the possibility to produce precision gyroscopic sensors that present important advantages over their macro-scale counterparts, such as lower cost and lower power consumption. These benefits have fueled an intensive worldwide research in the area, which explains why the performance of gyroscopes has improved by a factor of 10 every two years since 1991, when the Charles Stark Draper Laboratory demonstrated the first micromachined gyroscope [1]. The high demand for microgyros is due to their extensive applications, which range from automotive ride stabilization and rollover detection to virtual reality and military implementations.
II. OPERATION PRINCIPLES OF VIBRATING GYROS
A gyroscope follows Newton’s laws of motion, the first of which states that, in order to change the velocity vector of a moving mass, the application of a force is required. The second law states that the greater a mass the more resistant it is to change its velocity vector. A gyroscope is thus constructed by taking a body and suspending it about its center of mass in a frictionless support that allows for three degrees of angular freedom while having three degrees of constraint (i.e. for linear motion); such a device can therefore provide information about the angular orientation of its frame with respect to its moving mass [2].
Gyroscopes can be classified in three basic types [3]:
a)Spinning mass: is the classical gyroscope that has a mass spinning steadily with free movable axis (so called gimbal). When the gyro is tilted, the gyroscopic effect causes precession (motion orthogonal to the direction tilt sense) on the rotating mass axis, hence a change in angle can be detected.
b)Optical: lets laser ray reflect around many times within the enclosure.If the enclosure rotates, the duration between the emission of the laser to eventual reception will be different. The laser go-around can be done by mirrors inside the enclosure or by a coil of optical-fiber.
c)Vibrating Gyroscope: here a vibrating element, when rotated, is subjected to the Coriolis effect that causes secondary vibration orthogonal to the original vibrating direction. By sensing the secondary vibration, the rate of turn can be detected.
The classical macro-scale gyroscope employs a spinning wheel. Unfortunately, fabricating microscopic, low-friction bearings needed for this classical approach is impractical. Instead, an entirely different approach using a proof-mass mounted on a spring suspension is utilized in microgyroscopes [4]. Rather than spin as a conventional gyroscope rotor, the proof-mass vibrates back and forth in translational motion, as shown in Figure 1.
Figure 1: Schematic of a vibrating gyro
In this basic configuration, the proof mass is first put into oscillation in the x-axis (drive axis), parallel to the substrate. Once in motion, the proof-mass is sensitive to angular rotation about the z-axis, perpendicular to the substrate. This rotation thus induces a Coriolis acceleration in the y-axis (sense axis).
All vibrating gyroscopes rely on the phenomenon of the Coriolis acceleration. This acceleration is experienced by a body undergoing linear motion in a frame of reference that is rotating about an axis perpendicular to that of the linear motion. The resulting acceleration, which is directly proportional to the rate of turn, occurs in the third axis that is perpendicular to the plane containing the other two axes [5]. This coupling is the Coriolis effect and is given by:
Fc = 2mv (1)
which is the force produced when a vibratory mass m, moving at a velocity v, is placed in a rotation, [6].
Because the Coriolis effect manifests in a direction orthogonal to the vibratory motion, two degrees of mechanical freedom are required in a micromachined gyroscope, one for the drive and one for the sensing motion. As illustrated in Figure 1, any microgyroscope can be broken down into four main parts: the proof mass, an elastic spring, a dashpot and some method to measure the displacement of the mass. The proof mass is used to generate the inertial force after angular rotation is experienced by the gyro, and the spring is necessary to mechanically support the mass and return it to its original position after the acceleration ceases. The dashpot is usually the air captured inside the device and is important for controlling the motion of the mass (damping). Finally, the sense method is essential for detecting the induced motion (which is typically very small) by means of converting it into some electrical output.
The two most common sensing methods are capacitive and piezoresistive. The first simply involves measuring the change in capacitance between the proof mass and a fixed electrode when a displacement is originated. The second method relies on the property that piezoresistive materials have of experiencing a change in resistivity as a direct result of elongation or contraction. Thus by measuring such change in resistivity of piezoresistive materials deposited on the beams (or spring) that support the mass, its motion can be detected.
III. PERFORMANCE AND DESIGN ISSUES
The most important factors in determining the performance of a gyroscope are: scale factor, zero-rate output (ZRO), resolution and drift [7]. Scale factor is defined as the amount of change in the output signal per unit change of rotation [V/(/s)]. The ZRO, on the other hand, represents the output of the device in the absence of angular rate. This output is the sum of white noise and a slowly varying function. The white noise defines the resolution [(/s)/Hz], and the peak-to-peak value of the slowly varying function defines the drift of the gyroscope [/s].
Vibratory gyroscopes can be operated open or closed loop. In the open loop mode, the response is not instantaneous because some time is required for the amplitude of the sense mode to reach its steady state value. This time is approximately equal to 2Q/ [8], and it limits the bandwidth of the sensor to a few hertz. To obtain larger bandwidth, gyroscopes can be operated with a slight mismatch in the resonant frequencies of the sense and drive modes, but at the cost of reduced sensitivity [9].
On the other hand, in the closed loop mode of operation, the amplitude of the sense mode is continuously monitored and driven to zero. The bandwidth can then reach higher values than the open loop mode even with matching resonance and is only limited by the electronics. With matched resonant modes, assuming the electronic noise Vn has a white spectrum around the resonant frequency and that the detection circuit has a bandwidth BW, the minimum detectable electronic signal for a capacitive device can be expressed by [1]
(2)
This equation illustrates how lowering the resonant frequency, parasitic capacitance and noise of the circuit, and increasing the quality factor and Coriolis-induced capacitance change, would improve the resolution. It is important to note that, although the resonant frequency should be minimized, it also must be maintained above environmental noise (>2 kHZ) [1].
IV. HARPSS VIBRATING RING GYROSCOPE
In the past few years, research has been done on vibratory gyroscopes since there are many applications for these devices. Researchers at the University of Michigan have developed a vibrating ring gyroscope, schematically shown in Figure 2. This device consists of a vibrating ring, semicircular support springs, and drive, sense, and control electrodes, which are located around the structure. It is fabricated through the high aspect-ratio combined poly and single-crystal MEMS technology (HARPSS).
Due to symmetry factors, at least eight support springs are needed to result in a balanced ring with two identical flexural modes that have equal natural frequencies and are 45 apart from each other (see Figure 3) [8]. Each support spring has two electrodes, one to sense the motion and one to electrostatically drive the ring. This electrostatic force vibrates the ring in an in-plane elliptically shaped primary flexural mode with fixed amplitude. When the device is rotated around its normal axis, energy is transferred to the secondary mode from the primary mode, which increases the amplitude in the secondary mode. This buildup is capacitively monitored.
Figure 3: Flexural Modes of Vibration [8].
The amplitude of the sense mode is proportional to the rotation rate and is given by [8]:
(3)
where
Ag 0.37angular gain of the ring structure (which depends on the geometry of the sensor and is very stable over temperature and lifetime of the device);
Qquality factor of the mechanical structure;
0angular flexural resonance frequency;
qdrivevibration amplitude of the drive mode;
zrotation rate.
The vibrating ring structure also compares favorably to other vibratory gyroscopes. It is less temperature sensitive since both vibration modes change similarly as the temperature changes. Also, the quality factor, Q, directly amplifies the sensitivity since the resonant frequency is the same in both modes [1]. Furthermore, environmental vibrations can only cause a non-desired response if the mass or stiffness of the ring is asymmetrical. If the ring is symmetrical, then the non-desired vibrations will be filtered out. The device can overcome built in asymmetries by electronically compensating to balance the structure [10].
A. Fabrication Process
The fabrication process for a gyroscope using HARPSS technology is shown in Figure 4. HARPSS is a mixed-mode fabrication technology that combines features of bulk micromachining with surface micromachining. First step, deposit and pattern a thin layer of LPCVD silicon nitride underneath the electrode bonding pads. This serves as an isolation dielectric layer [8]. Next, dry etch into a silicon substrate using the STS Silicon Deep Reactive Ion Etcher (DRIE) to form deep trenches with smooth and straight sidewalls. Then deposit a sacrificial oxide layer and refill the trenches with polysilicon. Dope the polysilicon layer with boron to speed its etch rate [11]. Then, use a dry directional/isotropic SF6 silicon etch to release silicon sense electrodes that are as tall as the ring structure [11]. This involves a deep, directional etch followed by an isotropic SF6 silicon etch. Using HF:H2O , etch away the sacrificial oxide to create capacitive air gaps between the sense-electrodes and the ring structure [11].
Figure 4. Fabrication process for HARPSS gyroscope [11].
This technology has been successfully used to fabricate numerous thick polysilicon vibrating gyroscopes. Typical dimensions of a gyroscope using this method are around 1.1mm ring in diameter and 80 m tall [10].
B. Performance
This device provides several important features required for high-performance gyroscopes, including small ring-to-electrode gap spacing (<1 m) for increasing the sense capacitance; large structural height for increasing the radius and sense capacitance and reducing the resonant frequency; and a better structural material (polysilicon) for increasing the quality factor Q with an orientation-independent Young’s modulus [1].
An 80 m tall prototype polysilicon ring gyroscope was tested open loop under a vacuum. The sensitivity of the device under poor vacuum and large parasitics was measured to be 200 V/deg/sec [11]. The resolution was found to be approximately 1 deg/sec for a material quality factor of 1200. However, improvement in the material quality factor will reduce the resolution to 0.01 deg/sec in a 1 Hz bandwidth [11]. The minimum detectable signal that can be achieved in a 10 Hz bandwidth is 5x10-3 deg/sec [10].
C. Applications
High-performance microgyroscopes are needed in many different applications, including inertial navigation, control, defense, and avionics. HARPSS fabricated gyroscopes are best used in “rate grade” applications, which require a rotation rate resolution and bias stability of about 0.5 deg/s [10]. Applications in the automotive industry are traction control systems, ride stabilization, and roll-over detection. Consumer applications in electronics include stabilization of pictures in digital video cameras and inertial mice in computers. Applications that require improved performance, such as guidance of missiles, are not usually best suited with a HARPSS vibrating ring gyroscope.
D. Limitations
To obtain a high mechanical quality factor and improved resolution, both external and internal energy losses should be minimized. One of the typical problems encountered in the design of the HARPSS gyroscope that causes energy loss is the anchor problem. Excessive undercut of the silicon substrate at the post (see Figure 5) causes the interface oxide layer between the substrate and structural poly to be exposed during the HF release and get etched away, which in turn will result in a soft anchor that dissipates energy [10].
Figure 5: SEM view of the anchor of a poly ring gyroscope. Excessive undercut of the post can result in dissipation of energy.
Another possible source of dissipation of energy in trench-refilled polysilicon beams are voids and keyholes that can be generated during the polysilicon refill process, as shown in Figure 6. In order to avoid this problem, trenches with completely vertical (or slightly slanted inward) sidewall profile are needed and enough polysilicon needs to be deposited to completely refill trenches at the wide intersection points [10].
Figure 6: Voids and keyholes generated during the polysilicon refill process.
Finally, an important limitation worth mentioning in the HARPSS process is the RIE lag effect. The height of high aspect-ratio narrow trenches is usually less than the height of medium and wide trenches due this RIE lag. When etching 12 m wide trenches to a depth of 220 m, 5 m wide trenches would only etch to a depth of 175 m, lagging about 45 m or 20% (Figure 7). This reduces to 9% for 70 m deep trenches [11].
Figure 7: RIE lag effect.
V. DRAPER LABORATORY TUNING FORK GYROSCOPE
Tuning forks are a classical example of vibratory gyroscopes. The tuning fork, as illustrated in Figure 8, consists of two tines that are connected to a junction bar. In operation, the tines are differentially resonated to a fixed amplitude, and when rotated, Coriolis force causes a differential sinusoidal force to develop on the individual tines, orthogonal to the main vibration. This force is detected either as differential bending of the tuning fork tines or as a torsional vibration of the tuning fork system. The actuation mechanisms used for driving the vibrating structure into resonance are primarily electrostatic, electromagnetic, or piezoelectric. To sense the Coriolis-induced vibrations, capacitive, piezoresistive, or piezoelectric detection mechanisms are used. Optical detection is feasible, but generally too expensive to implement [1].
Figure 8: Tuning Fork Vibratory Gyroscope [1].
The Charles Stark Draper Laboratory has developed a vibratory tuning-fork rate gyroscope that is fabricated on silicon chips. Draper has had a strong history with MEMS inertial sensors and has made great strides in simplifying the fabrication process as well as improving the performance of their gyroscopes. Draper has been inventing inertial guidance systems for earth and space applications for over 50 years [12]. In 1993, they were the first to demonstrate rate sensing with a micromachined silicon sensor.
The gyroscope’s operation is shown in the schematic of Figure 9. Electrostatic forces are generated by exciting the combs and do not depend on the lateral position of the masses. This improves the sensitivity of the gyroscope due to the large amplitude vibrations. The gyroscope’s design is a silicon structure suspended above a glass substrate containing metallization deposited for sensor interfacing. The silicon structure contains two masses suspended by a sequence of beams anchored to the glass substrate [13]. When voltages are applied to the outer motor drives, the two masses are electrostatically forced to generate lateral, in-plane oscillatory motion. This in-plane vibration results in the drive velocity V [4].
Figure 9: Schematic drawing of the comb-drive tuning fork gyroscope, showing input rate , Coriolis forces F1 and F2, and horizontal drive velocity V [4].